An hp-adaptive pseudospectral method for solving optimal control problems
An hp-adaptive pseudospectral method for solving optimal control problems
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DOI：
10.1002/oca.957
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发表时间：
2011-07-01
影响因子：
1.8
通讯作者：
Rao, Anil V.
中科院分区：
文献类型：
--
作者：
Darby, Christopher L.;Hager, William W.;Rao, Anil V.
提出了一种 HP 自适应伪谱方法来数值求解最优控制问题。本文提出的方法迭代地确定段的数量、每个段的宽度以及每个段所需的多项式次数，以获得用户指定精度的解。从状态的全局伪谱近似开始，在每次迭代中，该方法确定分段中断的位置以及每个分段中的多项式次数，以供下一次迭代使用。段的数量和每个段上的多项式的次数继续更新，直到满足用户指定的容差。使用术语“hp”是因为每个段中的段宽度（表示为 h）和多项式次数（表示为 p）是同时确定的。研究发现，与全局伪谱方法相比，本文开发的方法可以用更少的计算量和内存获得更高精度的解决方案。因此，在全局伪谱方法在计算上难以处理的情况下，该方法使得使用伪谱方法解决复杂的最优控制问题成为可能。最后，该方法的实用性在不同复杂性的各种问题上得到了证明。版权所有 (C) 2010 约翰·威利父子有限公司
An hp-adaptive pseudospectral method is presented for numerically solving optimal control problems. The method presented in this paper iteratively determines the number of segments, the width of each segment, and the polynomial degree required in each segment in order to obtain a solution to a user-specified accuracy. Starting with a global pseudospectral approximation for the state, on each iteration the method determines locations for the segment breaks and the polynomial degree in each segment for use on the next iteration. The number of segments and the degree of the polynomial on each segment continue to be updated until a user-specified tolerance is met. The terminology 'hp' is used because the segment widths (denoted h) and the polynomial degree (denoted p) in each segment are determined simultaneously. It is found that the method developed in this paper leads to higher accuracy solutions with less computational effort and memory than is required in a global pseudospectral method. Consequently, the method makes it possible to solve complex optimal control problems using pseudospectral methods in cases where a global pseudospectral method would be computationally intractable. Finally, the utility of the method is demonstrated on a variety of problems of varying complexity. Copyright (C) 2010 John Wiley & Sons, Ltd.